Defending champion Alberto Contador finished 80 seconds down because of a mass crash involving a spectator 9km from the finish.
Belgian national champion Gilbert, who won three classics races in April, sped ahead from the pack in the final several hundred metres and kissed his jersey as he crossed the line.
"It was the last 500 metres, I had a lead ... (and) I went for it," Gilbert said. "It was an extreme effort and I was able to take advantage."
Gilbert, who has notched 13 victories between race and stage wins this year, had been a favourite to win the opening stage.
He clocked 4 hours, 41 minutes, 31 seconds for the sun-baked 191.5km ride from La Barre-de-Monts to Mont des Alouettes in the western Vendee region.